数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (1): 162-174.doi: 10.1016/S0252-9602(13)60133-2

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NOTES ON THE RESCALED SASAKI TYPE METRIC ON THE COTANGENT BUNDLE

Aydin GEZER|Murat ALTUNBAS   

  1. Department of Mathematics, Faculty of Science, Ataturk University, 25240, Erzurum-Turkey; Department of Mathematics, Faculty of Science and Art, Erzincan University, 24030, Erzincan-Turkey
  • 收稿日期:2012-09-17 出版日期:2014-01-20 发布日期:2014-01-20

NOTES ON THE RESCALED SASAKI TYPE METRIC ON THE COTANGENT BUNDLE

Aydin GEZER|Murat ALTUNBAS   

  1. Department of Mathematics, Faculty of Science, Ataturk University, 25240, Erzurum-Turkey; Department of Mathematics, Faculty of Science and Art, Erzincan University, 24030, Erzincan-Turkey
  • Received:2012-09-17 Online:2014-01-20 Published:2014-01-20

摘要:

Let (M, g) be an n-dimensional Riemannian manifold and T*M be its cotan-gent bundle equipped with the rescaled Sasaki type metric. In this paper, we firstly study the paraholomorphy property of the rescaled Sasaki type metric by using some compati-ble paracomplex structures on T*M. Second, we construct locally decomposable Golden Riemannian structures on T*M. Finally we investigate curvature properties of T*M.

关键词: almost paracomplex structure, cotangent bundle, Golden structure, para-holomorphic tensor field, Riemannian curvature tensor, scalar curvature

Abstract:

Let (M, g) be an n-dimensional Riemannian manifold and T*M be its cotan-gent bundle equipped with the rescaled Sasaki type metric. In this paper, we firstly study the paraholomorphy property of the rescaled Sasaki type metric by using some compati-ble paracomplex structures on T*M. Second, we construct locally decomposable Golden Riemannian structures on T*M. Finally we investigate curvature properties of T*M.

Key words: almost paracomplex structure, cotangent bundle, Golden structure, para-holomorphic tensor field, Riemannian curvature tensor, scalar curvature

中图分类号: 

  • 53C07